Combinatorial dna taggants and methods of preparation and use thereof

ABSTRACT

DNA taggants in which the nucleotide sequences are defined according to combinatorial mathematical principles. Methods of defining nucleotide sequences of the combinatorial DNA taggants, and using such taggants for authentication and tracking and tracing an object or process are also disclosed.

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

This application is a continuation of U.S. non-provisional patentapplication Ser. No. 14,251,690 filed Apr. 14, 2014, which is acontinuation of U.S. non-provisional patent application Ser. No.12/984,695 filed Jan. 5, 2011 and issued as U.S. Pat. No. 8,735,327,which claims the benefit of U.S. provisional patent Application No.61/292,884 filed Jan. 7, 2010, the disclosures of which are incorporatedherein by reference. The above benefit and priority claims are beingmade in an Application Data Sheet submitted herewith in accordance with37 C.F.R. 1.76 (b)(5) and 37 C.F.R. 1.78.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with United States Government support. The U.S.Government has a paid-up license in this invention and the right underlimited circumstances to require the patent owner to license others onreasonable terms as provided for by the terms of Contract No.FA8750-07-00089 awarded by the United States Air Force, Air ForceMaterial Command, Air Force Research Laboratory/IFKF and NationalScience Foundation, Small Business Innovation Research (SBIR) Award No.IIP-0944491.

REFERENCE TO A SEQUENCE LISTING

This application is being filed electronically via the USPTO EFS-WEBserver, as authorized and set forth in the Manual of Patent ExaminingProcedure § 1730 II.B.2(a)(A), and this electronic filing includes anelectronically submitted sequence (SEQ ID) listing. The entire contentof this sequence listing is herein incorporated by reference for allpurposes. The sequence listing is identified on the electronically filed.txt file as follows:

FILE NAME DATE OF CREATION SIZE 201904xx_JEA104_SL.txt Jan. 4, 201122,314 bytes

BACKGROUND Field of the Invention

Taggants utilizing DNA nucleotide sequences, and methods of making,combining and using such taggants.

Description of Related Art

There is an increasing commercial and national need for safe, covert andinformation-rich marker or “taggant” technology, which can be used inapplications such as protecting the public interest, preventing productcounterfeiting and piracy, and providing an evidentiary basis to enforceintellectual property rights or defend against unwarranted productliability litigation. There is a need for taggant technology that cangenerate and detect millions of distinct taggants, and decipher thebillions of distinct ways that these taggants can be combined. This needis illustrated in the following broad examples.

The United States Department of Commerce indicates that counterfeitingand piracy cost the U.S. economy between $200 billion and $250 billionper year, are responsible for the loss of 750,000 American jobs, andpose a threat to public health and safety. The FDA alone has seen an800% increase in the number of new counterfeit drug cases between 2000and 2006. The Center for Medicine and the Public Interest estimates thesales of counterfeit drugs will reach $75 billion in 2010. Thecounterfeiting of the drug heparin has been linked to the deaths ofbetween 81 and 149 people in the U.S., and resulted in hundreds ofallergic reactions.

Heretofore, a number of patents and publications have disclosed the useof taggant technology, wherein small quantities of certain substancesare used as taggants (markers or labels) for tagging, authenticating,tracking, and/or tracing other materials, items, or processes. Amongsuch disclosures are the following, all of which are incorporated hereinby reference:

U.S. Pat. No. 5,451,505 to Dollinger discloses methods for tagging andtracing materials using nucleic acids as taggants. In particular,Dollinger discloses a method for tagging a material by treating thematerial with a nucleic acid taggant so that the nucleic acid attachesto the material in an amount sufficient for subsequent detection. Thenucleic acid taggant comprises a specific nucleotide sequence or has adistinct composition of specific nucleotides to facilitate tracing.

International patent application publication WO/2000/061799 of Minton etal. discloses a method of marking a material and subsequently detectingthat it has been marked. The method comprises adding or applying amarker comprising a nucleic acid tag to the material, sampling a portionof the material containing the marker, and detecting the presence ofnucleic acid tag in the sample. The method is characterized in that thequantity of the nucleic acid tag present in the sample is determined toprovide an indication of the quantity of marker present in the material.

U.S. Pat. No. 7,112,445 to Welle discloses a method for identificationtagging, and in particular, identification tagging of ammunition. Anisotopic taggant is deposited in a layer at the interface between theammunition primer and propellant so that, as the ammunition is fired,the taggant is dispersed throughout the propellant. The taggant is thuscontained in the gunshot residue formed during the firing, and can beread by analysis of residue particles. Reading may be accomplished byemploying a binary coding system and a system of authentication tags.The required large number of unique identification tags are obtained byusing a fragmented coding system wherein each particle encodes only aportion of an ammunition serial number.

These and other taggant systems notwithstanding, certain problems remainunaddressed in the use of taggants to monitor bulk materials, items, andprocesses for their manufacture. Depending upon the particularapplication, a taggant needs to satisfy a broad range of requirements,some of which heretofore have been in conflict with each other. Thefollowing is a list of attributes that are desirable in a taggant and/ora set of taggants:

-   1. Having tens of thousands of unique “signatures” (numerical    sequences) in the set of taggants for authenticating, and/or    tracking and tracing a large number of targets with a large quantity    of aspects (i.e. bits of data).-   2. “Deeply layerable,” i.e. it should be possible to tag an object    with multiple taggants (either simultaneously or over time), wherein    the object has undergone a series of manufacturing process steps,    and/or is comprised of multiple materials possibly from multiple    production batches, and/or is comprised of items that may be from    multiple manufacturing plants or suppliers. These are exemplary    characteristics; an object may have other characteristics that can    be correlated with taggants. The “layered taggants” can be provided    on or in the object to represent its various characteristics. The    identity of each of the taggant in the layered collection of    multiple taggants must be recoverable from the object, and capable    of being detected, and analyzed and decoded such that the object can    be authenticated, and/or its production history tracked and traced.-   3. Nano-scale (i.e. on the order of nanometers dimensionally). This    enables taggants to be applied to extremely small structures or    items, as well as being covert.-   4. Highly covert, i.e. undetectable to an observer, or even    undetectable by analysis when it is known or suspected that a    taggant is present, but no knowledge of the taggant nature or code    is available.-   5. Detectable at a parts-per-trillion concentration. This enables    low cost use, in that a very small amount of taggant is required to    be applied on or in an object to enable subsequent authentication    and/or track and trace. Additionally, this attribute facilitates    highly covert use.-   6. Efficiently decodable, so that the information contained in a    taggant, or layered taggants, is easily and quickly accessed.-   7. Inert, non-reactive, so that they can be used in a broad range of    environments with no interaction with chemicals, heat, light, etc.    that are present in an ambient environment.-   8. Ingestible, so that they can be used on ingestible products, such    as medications.-   9. Environmentally safe, so that in use, they do not contaminate an    environment or product to which they are applied.-   10. Not harmful to internal combustion engines.-   11. Useable in solution. By being soluble in a common liquid medium,    they can be easily applied in small quantities by simple dispensing    equipment.-   12. Useable in solids or on solid surfaces, so that they can be    easily integrated into an object, or applied to the object.-   13. Inexpensive, so that the cost of the taggant is insignificant    compared to the cost or value of the product to which it is applied.

In summary, there is both a market need and, in some instances, alegislative imperative for track, trace-back, and authenticationtechnologies. In the field of pharmaceuticals, for example, the Food andDrug Administration Amendments Act (FDAAA) of 2007 directs the FDA toidentify and validate effective technologies for the purpose of securingthe drug supply chain and for the development of standards for theidentification, authentication, and tracking and tracing of prescriptiondrugs.

It is an extremely challenging problem to provide a taggant or set oftaggants that has all of the above attributes, or even a large majorityof them, in order to satisfy the stringent requirements of complexapplications such as pharmaceuticals. To the best of the Applicant'sknowledge, there is no taggant currently available which has all of theabove listed attributes. There remains a need for such a taggant forproviding protection of products and/or processes in fields such asagriculture, banking, defense, environmental protection, homelandsecurity, law enforcement, consumer products, transportation, and publichealth.

More specifically, as will be explained subsequently herein with regardto the art of DNA taggant technology, small taggant libraries of DNAtaggants having relatively short sequences are of limited use inpractical applications; and substantially larger desirable taggantlibraries having longer sequences needed for bit depth (informationcontent) are extremely difficult to synthesize and are cost-prohibitive.What is needed in this art is a set of DNA taggants that aresufficiently short that they can be provided cost-effectively, whilealso containing the desired large amount of information in a particularapplication.

SUMMARY

The present invention meets these needs by providing DNA taggants inwhich the nucleotide sequences are defined according to principles ofcombinatorial mathematics. In accordance with the invention, methods ofmaking combinatorial DNA taggants are also provided.

In certain embodiments, a combinatorial DNA taggant in accordance withthe invention is provided having a polymerase chain reaction responsesignal identical to the polymerase chain reaction response signal of anidealized and much longer DNA taggant that is expensive and difficult(or impossible) to synthesize. A method of making a set of such taggantscomprises creating a library of idealized DNA taggants from a table ofnon-cross-hybridizing table-mer sequences, and performing acombinatorial analysis to identify a plurality of combinatorial coveringDNA strands to simulate the idealized DNA taggants of the library. Thecovering strands may then be synthesized, and they may then becombinatorially mixed.

In other embodiments, a combinatorial DNA taggant is provided comprisingn(n−1)/2 unique bit register encoding strands produced fromconcatenating n unique DNA table-mers and their reverse complements. Amethod of making such a taggant comprises defining the set of n singlestranded DNA table-mers and their reverse complements, each of thetable-mers being different from the other table-mers; and preparing theset of n(n−1)/2 unique bit register encoding strands by concatenatingthe n single stranded DNA table-mers and their reverse complements.Subsets of the n(n−1)/2 unique bit register encoding strands may beselected as the combinatorial DNA taggants. Each of the uniquecombinatorial DNA taggants may be used to represent a unique binarynumber.

The Applicant's combinatorial method of DNA taggant design and detectionenables encoding product, item, or process information as aalpha-numeric sequence represented in DNA in a manner analogous to how acomputer stores information in a spreadsheet. This DNA data structurecan be read by the laboratory polymerase chain reaction (PCR) method,and then algorithmically decoded to retrieve virtually an unlimitedamount of product, item, or process information that has been stored inthe instant combinatorial DNA taggants. These taggants can be used toforensically mark objects for anti-counterfeiting, brand protection,liability protection, and other similar security applications.

By virtue of their engineered design, the Applicant's syntheticcombinatorial DNA taggants, abbreviated “ComDTags” subsequently herein,are functional at concentrations down to 0.25 parts per trillion. Thus,they cannot be reverse engineered because their detection is onlypossible with prior knowledge of the taggant-specific DNA sequencesrequired for PCR amplification. The Applicant's DNA taggants differ fromall other DNA-based taggants due to the Applicant's combinatorialmethod, which provides an engineering capability to easily constructmillions of unique DNA taggants. In contrast, the current technologyknown to the Applicant can only obtain on the order of hundreds ofuniquely decipherable, and primarily genomic DNA taggants. The easilyconstructed millions of Applicant's combinatorial DNA taggants areunique, information-rich, and able to be used covertly, providingtaggant “signatures,” i.e., number patterns and sequences that representinformation, that uniquely identify the items and/or processes theylabel. These signatures can be detected and decoded only by authorizedusers.

One aspect of the invention is the combination of mathematics andmolecular biology to produce the combinatorial DNA taggants. Mathematicsis used to design the synthetic DNA that makes the storage ofinformation in ComDTags possible. Then, the specificity of DNA strandrecognition and the wet laboratory method of polymerase chain reaction(PCR) is used to generate signals indicative of DNA taggants beingpresent. Finally, mathematics is used to decode the PCR signals andidentify the taggant (or layered taggant) signatures and the informationthey contain.

The information gained by employing ComDTag signatures can be used toprevent counterfeiting and to authenticate, and/or track and trace-backdrugs, documents, brand names and manufacturing processes. Moreover, thetrack and trace-back utility of ComDTag signatures can aid in theprediction, detection and resolution of homeland security threats.Government-issued documents (e.g., passports or currency) may use aComDTag signature as the unique, forensically covert identifier thatmatches only one serial number. ComDTags embedded in currency could helpto trace money laundering or track the money path of organized crime orterrorist financing. Being stable, non-reactive, covert, and able to beapplied on site, ComDTags are well-suited for tagging explosives andtheir components. Forensics experts investigating terrorist activitiescould trace such explosives back to a particular store, manufacturingplant and/or geographic location. Being ingestible, ComDTags would bewell-suited for tagging drugs and addressing the requirements of theaforementioned FDAAA.

All of the above taggant applications may be enhanced by taggantlayering. In certain embodiments, taggant layering may be a combinationof an instantaneously detectable overt taggant, and information-rich,highly unique, superimposable and deeply covert taggants such ComDTags.Taggant layering enables a quick initial authentication via the overttaggant, plus a forensic authentication with track and trace-backcapability via the instant ComDTags. Accordingly, ComDTags cansignificantly enhance the utility of existing overt taggants, and thusare especially well-suited to address all of the above exemplary taggantapplications. The Applicant's combinatorial DNA taggant system enablesdecoding of the identity of each ComDTag in a multiple and layeredComDTag signature. This unique ability makes the instant combinatorialDNA taggant system ideal for taggant layering. Through taggant layeringdecoding, the instant ComDTags can be used to track not only individualcomponents, but they can also be used to trace back and authenticatemulti-stage manufacturing processes and supply chains. To the best ofthe Applicant's knowledge, no other nano-scale and covert taggant systemhas this capability at any cost.

In general, the decoding of process taggant layering has been anintractable problem for target processes and objects requiring deeplylayered taggants. However, with the instant ComDTags being constructedin a combinatorial manner, the decoding of such deeply layered taggantsfor a process is feasible. Thus, in addition to being covert andinformation-rich, the instant combinatorial DNA taggants may also beused for both item and process taggant layering.

One exemplary application of the instant ComDTags is their use intagging other more overt, but instantaneously detectable, taggants. Suchovert taggants may be e.g., phosphors, radio frequency identifications(RFIDs), holograms or barcodes. One or more ComDTags and an existingovert taggant may be used together to provide taggant layering of atarget. For example, consider the packaging of a pharmaceutical drug.Being theoretically safe for human consumption, covert and nano-size,ComDTags may be used to label the pills in a container, and/or the foilseal for the container. Then the pill container itself (e.g., box, vile)may be taggant layered with both an existing overt tag and a ComDTag. Ina subsequent inspection, the overt taggant may be quickly scanned toreveal whether or not the packaging is authentic. Then, to authenticatethat the pills in the container are indeed the ones intended to bethere, a deeper level of authentication can reveal whether or not theDNA on the pills matches the DNA in the layered taggant on the outsideof the box and/or the foil seal. Additionally, the associated ComDTagdecoding methods can also discover the absence of a ComDTag, and therebydiscover a missing legitimate ingredient or step in the targetcombination of container and pills.

The pharmaceutical authentication protocol in the above example may befurther extended by the deeper layering capabilities of the instantComDTags. Consider that a manufacturer not only wants a final pillproduct to be labeled with a taggant, but also wants to ensure that thepill was produced in a legitimate manner with legitimate ingredients andsupplies. If a unique ComDTag signature is used to identify eachimportant stage and ingredient, then the final pill is taggant layeredwith the conglomerate of the ComDTags for the process. This taggantlayering can in turn be used to tag the overt taggant. Thus, the instantComDTags can not only be used to authenticate the pills in thecontainer, they can also simultaneously authenticate the productionprocess thereof. This authentication capability is especially importantto a company that want to enhance public safety, while simultaneouslyprotecting itself against unwarranted product defect litigation, sinceDNA has been established as a highly reliable form of evidence in legalproceedings.

In summary, the Applicant's combinatorial methods provide DNA taggantsthat are in far greater numbers, are less expensive, carry more iteminformation, are more covert, and are more layerable than all othercovert taggants known to the Applicant. Details on the instantcombinatorial DNA taggants, methods of providing them, and examples oftheir use are explained subsequently herein.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure will be provided with reference to the followingdrawings, in which like numerals refer to like elements, and in which:

FIG. 1 depicts an exemplary double stranded DNA taggant (SEQ ID NO: 11)that can be used to represent an alpha-numeric sequence;

FIG. 2 is a flowchart depicting one embodiment of the Applicant's methodof defining a set of combinatorial DNA taggants, and using such taggantsin determining authenticity and/or performing trace back of a targetobject or process;

FIG. 3A is an example of a network graph that may be used to define aset of combinatorial DNA taggants and a set of PCR reactions to read thecombinatorial DNA taggants according to the method depicted in FIG. 2(FIG. 3A discloses SEQ ID NOS 1-10, respectively, startingcounter-clockwise from the sequence labeled as “(0,0)”);

FIG. 3B depicts the network graph of FIG. 3A, modified to identify theset of positive PCR reactions for a specific and idealized DNA taggantrepresented by a particular alpha-numeric value (FIG. 3B discloses SEQID NOS 1-10, respectively, starting counter-clockwise from the sequencelabeled as “(0,0)”);

FIG. 4 is a network graph (with positive PCR reactions highlighted) ofan actual combinatorial DNA taggant (ComDTag) of the present invention,which is designed to produce the same PCR reactions as the taggantreferenced in FIG. 3B (FIG. 4 discloses SEQ ID NOS 1-10, respectively,starting counter-clockwise from the sequence labeled as “(0,0)”);

FIG. 5 is a network (sub)graph of the solely positive PCR reactions fora group of four layered taggants, given in FIG. 11, selected from ataggant library (FIG. 5 discloses SEQ ID NOS 1, 9-10, 8, 7, 6, 3-5 and2, respectively, starting counter-clockwise from the sequence labeled as“(0,0)”);

FIG. 6A is a network graph of all possible PCR reactions for a morecomplex combinatorial DNA taggant example that may be used according tothe method depicted in FIG. 2;

FIG. 6B depicts the network graph of FIG. 6A, modified to identify theset of positive PCR reactions for a specific and idealized DNA taggantrepresented by a particular alpha-numeric value;

FIG. 7 is a network graph (with positive PCR reactions highlighted) ofan actual combinatorial DNA taggant (ComDTag) that is designed toproduce the same PCR reactions as the taggant referenced in FIG. 6B;

FIG. 8 is an example of a network subgraph that shows only the edgesthat denote positive PCR reactions for a particular layered combinationof four actual combinatorial DNA taggants (ComDTags);

FIG. 9A is a electrophoresis gel image of exemplary combinatorial DNAtaggants in a laboratory demonstration of one embodiment of theinvention;

FIG. 9B is a dye based real-time PCR fluorescence image of exemplarycombinatorial DNA taggants in a laboratory demonstration of oneembodiment of the invention;

FIG. 10 is a network subgraph prepared in a laboratory demonstration ofFIG. 9A, and is essentially the same a FIG. 5 except reference tospecific sequences have been removed for simplicity of illustration;

FIG. 11 is a listing of the combinatorial DNA taggants (SEQ ID NOS87-90, respectively, in order of appearance) found to be present in thelaboratory demonstration, from an analysis of FIG. 9A and the networkgraph of FIG. 10;

FIG. 12 depicts an example of a method of encoding an alpha-numeric bitstring by mixing pairs of concatenated strands of DNA (SEQ ID NOS 73,75-76 and 78, respectively, in order of appearance) that represent bitregisters, the method useable with dye-based PCR;

FIG. 13 depicts an example of an alternative method of encoding analpha-numeric bit string by mixing triples of concatenated strands ofDNA (SEQ ID NOS 81, 83-84 and 86, respectively, in order of appearance)which represent bit registers, the method useable with probe-based PCR;and

FIG. 14 is a flowchart depicting a method of preparing a layered taggantcomprising a combinatorial DNA taggant and a non-DNA taggant.

The present invention will be described in connection with certainpreferred embodiments. However, it is to be understood that there is nointent to limit the invention to the embodiments described. On thecontrary, the intent is to cover all alternatives, modifications, andequivalents as may be included within the spirit and scope of theinvention as defined by the appended claims.

DETAILED DESCRIPTION

For a general understanding of the present invention, reference is madeto the drawings. In the drawings, like reference numerals have been usedwhere needed to designate identical elements.

As used herein, certain terms are defined as follows:

NUCLEIC ACID: a deoxyribonucleotide or ribonucleotide polymer in eithersingle- or double-stranded form. The nucleotides thereof may include thenaturally occurring nucleotide bases adenine, thymine, guanine,cytosine, and uracil, as well as non-naturally occurring nucleotidebases such as those incorporating inosine bases, and derivatizednucleotides, such as 7-deaza-2′deoxyguanosine, methyl- (or longer alkyl)phosphonate oligodeoxynucleotides, phosphorothioateoligodeoxynucleotides, and alpha-anomeric oligodeoxynucleotides.TAGGANT: In general, a marker placed on, or associated with, an item orprocess.DNA TAGGANT: A taggant made of deoxyribonucleic acid having a specificnucleotide sequence or a specific nucleotide composition.OVERT TAGGANT: A taggant that is detectable by visual inspection, or bya common hand-held instrument such as an ultraviolet lamp, or by asimple procedure such as heating the object containing the taggant.COVERT TAGGANT: A taggant that is not detectable by visual inspection orby a common hand-held instrument or by a simple procedure; instead,requiring specialized laboratory methods for detection.TAGGING: The process of treating an item or material with a composition,the taggant, for subsequent identification of the item or material bydetection of the taggant.TRACING: The process of determining the origin or source of an item ormaterial.TARGET: An item or process to which a taggant has been added orassociated.TAGGANT LAYERING: The association of multiple taggants to a target. Thetarget may be a single item, or a process, or an object comprised ofmultiple items produced by a process having multiple steps. Taggantlayering of a target item may be done by associating multiple taggantsto a single item. Taggant layering of a target process or objectproduced thereby may be done by placing one or more taggants on eachitem produced in a step in the process. The conglomerate of all taggantsin a process is the layered taggant for the process.

Background Information on DNA

As an introduction, the applicant provides the following summary ofbasic information on DNA, deoxyribonucleic acid. DNA is a nucleic acidthat encodes the genetic instructions used in the development andfunctioning of living organisms. DNA is a long polymer comprisingrepeating units called nucleotides. It may exist in single stranded form(ssDNA), or double stranded form (dsDNA). In living organisms, DNA isusually present in double stranded form, as a pair of single strandmolecules that are held tightly together in an entwined shape commonlyreferred to as “the double helix.”

In a single stranded of DNA, the repeating nucleotide units contain boththe segment of the backbone of the molecule, which holds the chaintogether, and a base. The backbone consists of alternating phosphate andsugar entities. The sugar in DNA is 2-deoxyribose, a pentose(five-carbon) sugar. The sugars are connected by phosphate groupsbetween them, which form phosphodiester bonds between the third andfifth carbon atoms of adjacent sugar rings. These asymmetric bondsprovide a reference direction or orientation that can be referred towhen describing a single strand of DNA.

The repeating unit of DNA, the nucleotide, consists of a base linked toa sugar and one or more phosphate groups. A series of nucleotides linkedtogether may be referred to as a polynucleotide. In living organisms,these polynucleotide DNA molecules may consist of millions of nucleotideunits.

In naturally occurring DNA, any nucleotide in a strand has one of fourbases: adenine, thymine, guanine, and cytosine, abbreviated as A, T, G,and C, respectively. A single strand of DNA may be characterized by itsnucleotide sequence, with reference to the direction of the strand,i.e., whether the sequence is recited beginning from the 5′ end having aterminal phosphate group, or the 3′ end having a terminal hydroxylgroup. Thus the asymmetric ends of DNA strands are referred to as the 5′(five prime) and the 3′ (three prime) ends. Accordingly, the very shortDNA strand 5′AACG3′ differs from 5′GCAA3′, but is identical to 3′GCAA5′.

In doubled stranded DNA, the direction of the nucleotides in one strandis opposite to the direction in the other strand, such that at eitherend of the double stranded molecule, one strand terminates at the 5′end, and the other strand terminates at the 3′ end. Each type of base onone strand forms a bond with just one type of base on the other strandin a phenomenon known as complementary base pairing. The individual basepairs are joined by hydrogen bonding, with A bonding exclusively to T(and vice versa), and C bonding exclusively to G (and vice versa).Accordingly, any given single stranded DNA molecule can most easily formdouble stranded DNA with its “reverse complement” strand DNA, which hasthe exact nucleotide sequence such that along the double strand, onlyA-T pairs and C-G pairs occur. If the nucleotide sequence of a singlestrand of DNA is known, its reverse complement can easily be determined.To obtain the 3′ to 5′ reverse complement of a 5′ to 3′ strand of DNA,one simply substitutes A with T and vice versa, and C with G andvice-versa, reciting the base pairs in the 3′ to 5′ direction.

For example, the 3′ to 5′ reverse complement of 5′TCGCA3′ is 3′AGCGT5′.A double stranded DNA duplex formed between a single strand and itssingle strand reverse complement is commonly referred to as aWatson-Crick (WC) duplex. The length of single stranded DNA or a doublestranded DNA WC duplex is commonly expressed as the number of bases orbase pairs (bp), respectively, in the strand or duplex. The length isoften referred to using the shorthand suffix “-mer,” being short for“polymer.” For example, the strand TCGCA is called a “5-mer;” the lengthof the WC duplex

TCGCA ||||| AGCGTis 5 base pairs.

From this point forward in this disclosure, unless noted otherwise orexplicitly shown, all nucleotide sequences of DNA strands are recited inthe 5′ to 3′ direction. Method of Representing Numerical Sequences UsingDNA Nucleotide Sequences

Any finite alpha-numeric sequence can be encoded as a ssDNA (or dsDNA)taggant; and conversely, any ssDNA or dsDNA taggant may be expressed asa finite alpha-numeric sequence. In the following description, all lowercase variables such as e.g., n, q, s, and t are natural numbers, i.e.non-negative integers. As used herein, the term “alpha-numeric sequence”is meant to indicate any sequence of alphabetical letters or othersymbols in combination with numbers; or a sequence of alphabeticalletters or other symbols exclusively; or a sequence of numbersexclusively. The use of the terms “numerical” or “numeric” herein areintended to also include alphabetical letters or other symbols, unlessspecifically indicated otherwise.

Consider a fixed set of n·q relatively short single strands of DNA, eachhaving a length of t bases, i.e., a fixed set of “t-mers.” They may bearrayed in a table having n columns and q rows. This is referred toherein as “t-DNA n by q table code” and denoted using the notationDNA_TC(n,q,t). Table 1 is a simple example of such a table, expressedaccordingly as DNA_TC(5,2,10).

TABLE 1 Exemplary table according to table code DNA_TC(5,2,10).position 0 position 1 position 2 position 3 position 4 (SEQ ID NOS(SEQ ID NOS (SEQ ID NOS (SEQ ID NOS (SEQ ID NOS 1 and 6) 2 and 7)3 and 8) 4 and 9) 5 and 10) 0 CGTCCATCGT CATTCGCGGA ACAGTTGCCGTCGGTAAGCG GAGCGAACCA 1 GCAGAAGCCA CGCAAGCTGA AGTGGATGCG TGCACGAGACTCGGAGTGCT

The sequences in a given table DNA_TC(n,q,t) are also referred to hereinas “table-mers.” A single stranded DNA taggant library may be generatedfrom the table-mers. The library is the collection of q^(n) relativelylong nt-mer strands of single stranded DNA having lengths of n×t basepairs, which are concatenated from a given table DNA_TC(n,q,t). A memberof a single stranded DNA taggant library is referred to herein as anssDNA taggant (and as an idealized taggant).

The concatenated table-mers may be used to express any finitealpha-numeric sequence. For example, the table-mers from Table 1 may beused to express a series of 32 binary numbers, i.e., 2⁵, or q^(n) whereq=2 and n=5. The binary numbers thus range from 00000 to 11111. Using aspecific example, the binary sequence 01101 is encoded as

(SEQ ID NO: 11) CGTCCATCGT CGCAAGCTGA AGTGGATGCG TCGGTAAGCG TCGGAGTGCT.

Referring to Table 1, it can be seen that the first ten bases of thefifty base sequence is the ten base sequence of the 0 value of position0, (0,0); the second ten bases of the fifty base sequence is the tenbase sequence of the 1 value of position 1, (1,1); the third ten basesof the fifty base sequence is the ten base sequence of the 1 value ofposition 2, (2,1); the fourth ten bases of the fifty base sequence isthe ten base sequence of the 0 value of position 3, (3,0); and the fifthten bases of the fifty base sequence is the ten base sequence of the 1value of position 4, (4,1). In making this representation of the binarysequence, each of the table-mers in DNA_TC(5,2,10) may be identified byan ordered pair of (position, value) as shown above. The firstcoordinate of the pair corresponds to the position (column) and thesecond coordinate corresponds to the value (row).

Such encoding is possible because only certain collections of sequencesare allowed to be in each position (row), and within each collection,distinct strands are assigned distinct numerical values (e.g.,CGTCCATCGT=0 (SEQ ID NO: 1), GCAGAAGCCA=1 (SEQ ID NO: 6) for position0). The sequences are chosen such that they are sufficiently differentto prevent errors in analyzing the coding, as will be explained infurther detail subsequently herein.

It is straightforward to see that n·q table-mers can be used to make ann by q table, which in turn can be concatenated to make q^(n) distinctlonger DNA taggants encoding each numeric sequence with n digitpositions where each digit can range from 0 to q−1. As a furtherexample, a 3×7 table DNA_TC(7,3,12), wherein q=3, n=7, and t=12 consistsof 21 table-mers having lengths of 12 nucleotides, which can beconcatenated to produce a taggant library of 3⁷ (2187) distinct singlestrands of DNA having lengths of 84 nucleotides. This library can alsorepresent the number sequence from 0000000 to 2222222 (the numbersequence being in base 3).

For every single stranded DNA taggant there is a corresponding doublestranded DNA taggant that is the unique WC duplex that contains thesingle stranded DNA taggant duplexed with its reverse complement(single) strand. Referring to FIG. 1, it can be seen that a ssDNAtaggant can be identified with the unique WC dsDNA taggant that containsit (and its reverse complement). Accordingly, the term DNA taggant usedherein also includes WC dsDNA taggants. For a given DNA_TC(n,q,t) tablecode which is designated by the notation M, the notation TAG(n,q,nt) ofM may be used to denote the collection of q^(n) possible distinctdouble-stranded n·t base pair taggants that can be formed byconcatenation. These doubled stranded n·t base pair taggants are alsoreferred to herein as idealized taggants. In this notation convention,each DNA taggant is identified by its top strand, which is writtenleft-to-right in the 5′ to 3′ direction as shown in FIG. 1. Theexemplary DNA taggant 10 in FIG. 1, which represents the binary sequence01101 as described previously, is a member of TAG(5,2,50) of Table 1.

Polymerase Chain Reaction Laboratory Method

Polymerase chain reaction (PCR) is a technique widely used in molecularbiology, forensic science, environmental science, and many other areas.As is disclosed in Wikipedia athttp://en.wikipedia.org/wiki/Polymerase_chain_reaction, “The polymerasechain reaction (PCR) is a scientific technique in molecular biology toamplify a single or a few copies of a piece of DNA across several ordersof magnitude, generating thousands to millions of copies of a particularDNA sequence. The method relies on thermal cycling, consisting of cyclesof repeated heating and cooling of the reaction for DNA melting andenzymatic replication of the DNA. Primers (short DNA fragments)containing sequences complementary to the target region along with a DNApolymerase (after which the method is named) are key components toenable selective and repeated amplification. As PCR progresses, the DNAgenerated is itself used as a template for replication, setting inmotion a chain reaction in which the DNA template is exponentiallyamplified.

“Almost all PCR applications employ a heat-stable DNA polymerase, suchas Taq polymerase, an enzyme originally isolated from the bacteriumThermus aquaticus. This DNA polymerase enzymatically assembles a new DNAstrand from DNA building blocks, the nucleotides, by usingsingle-stranded DNA as a template and DNA oligonucleotides (also calledDNA primers), which are required for initiation of DNA synthesis. Thevast majority of PCR methods use thermal cycling, i.e., alternatelyheating and cooling the PCR sample to a defined series of temperaturesteps. These thermal cycling steps are necessary first to physicallyseparate the two strands in a DNA double helix at a high temperature ina process called DNA melting. At a lower temperature, each strand isthen used as the template in DNA synthesis by the DNA polymerase toselectively amplify the target DNA. The selectivity of PCR results fromthe use of primers that are complementary to the DNA region targeted foramplification under specific thermal cycling conditions.

The polymerase chain reaction technique is further described in ThePolymerase Chain Reaction, Mullis et al., Birkhäauser, Boston, 1994; andin U.S. Pat. No. 4,683,202 of Mullis, “Process for Amplifying NucleicAcid Sequences,” the disclosure of which is incorporated herein byreference.

The PCR technique may be used in detecting DNA taggants that have beenapplied on or in a target item for authentication and/or track and traceof the item. Consider a simple example in which one dsDNA (or ssDNA)taggant is selected from a taggant library TAG(n,q,nt) of idealizedtaggants, and applied to a target, such as a capsule containingmedicine. All capsules in a given manufacturing production lot aretargets and the single dsDNA taggant is applied to all capsules in thatlot. Subsequently, a sample of the medicine is purchased at a retailpharmacy under suspicion that it is counterfeit product.

A capsule of the sample under suspicion is tested using the PCRtechnique. Material from the capsule is subjected to the reagents usedin PCR, which include a pair of primers, each primer being a shortstrand of DNA that can bind to a complementary section of a relativelylong single strand of DNA, at which point the DNA polymerase that ispresent in the PCR reaction medium functions to add the complementarysequences of nucleotides, thereby completing the formation of the WCduplex of that long single strand of DNA. One of the primers is selectedto be complementary to the first of the two single strands of the dsDNAtaggant that was applied to the target medicine, and may be selected tojoin at or near the 3′ end of that single strand. The other of theprimers is selected to be complementary to the second of the two singlestrands of the chosen dsDNA taggant, and may be selected to join at ornear the 3′ end of that single strand.

If the capsule is genuine, i.e. not counterfeit, the chosen DNA taggantwill be present in the sample placed in the PCR reaction medium, andamplification of the DNA taggant will occur. In the PCR reaction, thedsDNA taggant separates, and the primers form partial duplexes withtheir complementary regions on each of the single strands. Nucleotidesare then added by the DNA polymerase in the 3′ to 5′ direction tocomplete the WC duplexes to their respective 5′ ends. If at most onlyone of the two primers used have complementary regions on the targetduplex, then essentially no amplification will be detected. If thecapsule is counterfeit, in one instance, there will be no DNA taggant,and no amplification will occur, thus confirming it is counterfeit. Inanother instance, even if it were known that DNA taggants were beingadded to the capsule, and the counterfeiters added some random sequencesof DNA to the counterfeit product, the odds of their selecting thecorrect sequences that would amplify with both primers is very small(approximately 1 in a trillion if primers are 20-mers).

The capsule or other targets may include multiple or “layered” taggants.For example, if the capsule contains first and second medications withina capsule wall, the first medication could include a first taggant, thesecond medication could contain a second taggant, and the solublecapsule wall could contain a third taggant. A sample of the capsule andits contained medications may be subjected to the PCR technique, inwhich three different pairs of primers may be used to amplify all threeof the respective taggants if they are present. If all three taggantsare not present, the capsule would be proven counterfeit. If less thanall three taggants are present, some improper activity is indicated,which can be investigated.

The chosen DNA taggant or taggants may be present in extremely lowconcentration on or in the target, as low as 0.25 parts per trillion,while still being detectable by amplification via the PCR technique.After amplification occurs in a sample, the exponentially increasedconcentration of the DNA taggant may be detected by various knownmethods. One standard method for detection of amplification known as gelelectrophoresis uses an electrical separation and detection of DNAsubstrands on a size separation gel medium. Other more sensitive andfaster (e.g., real-time PCR) methods that automate the entire PCRprotocol and can detect amplification are also known. For example, onemay use the dye based (e.g., Sybr-Green) or probe based (e.g., TaqMan®)real-time PCR methods from Applied Biosystems of Foster City, Calif.,that can be performed on suitable PCR apparatus (e.g., the Stratagene3000 MX Pro of Agilent Technologies Inc. of Santa Clara, Calif.; or theSmart Cycler® of the Cepheid Corporation of Sunnyvale, Calif.; or theAuto-Lid Dual 384-Well GeneAmp® PCR System of Applied Biosystems. Anexample of the experimental output from dye based PCR is given in FIG.9B. It can be seen that for the DNA taggants that are present, i.e.those having positive PCR signals, amplification results in stronglydetectable fluorescence in about 15-20 PCR cycles. In contrast, theprimer pairs that match DNA taggants that are not present produce no(i.e. negative) signal.

The preceding example serves to illustrate how the PCR method may beused in the detection of DNA taggants. For a set of relatively shorttaggants contained in a small taggant library, this example may beapplicable. Table 2 depicts an example of such a taggant library,TAG(5,2,50), created from table-mers of DNA_TC(5,2,10) of Table 1.

However, the short taggants and small taggant library of Table 2 arepresented herein only for illustration of certain basic concepts. Inpractice, the taggant library of Table 2 is of limited use for severalreasons. Firstly, the length t of the table-mers that are concatenatedto form the taggants are only 10 bases long. In order to have morereliability in the PCR method, it is desirable to have the table-mers besignificantly longer, on the order of 20-30 bases. Secondly, the bitdepth n of the taggants of Table 2 is only 5 digits. In manyapplications, it is desirable to have significantly greater bit depth,such as between 10 and 20 digits. Thirdly, the value q of the bits intaggants of Table 2 is binary, i.e. 0 and 1. In many applications, it isdesirable to have more than just binary values, i.e. q greater than 2.

It is also noted that except for very small sets of DNA taggants, agiven dsDNA taggant cannot unambiguously be identified simply throughthe use of a PCR primer pair that matches the respective 3′ ends of thestrands. For example, consider the previously discussed the binarysequence 01101 encoded as CGTCCATCGT CGCAAGCTGA AGTGGATGCG TCGGTAAGCGTCGGAGTGCT (SEQ ID NO: 11). A pair of primers is required to amplify theentire sequence, starting at the 3′ end of the above strand and at the3′ end of its reverse complement. The primer required for the 3′ end ofthe above strand is AGCACTCCGA (SEQ ID NO: 12). The primer required forthe 3′ end of the reverse complement of the above strand is CGTCCATCGT(SEQ ID NO: 13). However, these primers will also amplify any othernumber values beginning in 0 and ending in 1, i.e., 00001, 01001, 00101,00011, 01011, 00111, and 01111.

In like manner, different primer pairs would be needed to amplify thesequences 0xxx0, 1xxx0, and 1xxx1, where x may be 0 or 1. Each of theserepresents eight separate numbers. It will be apparent that a strategyof attempting to identify DNA taggants by only initiating amplificationat the ends of the strands will be insufficient, unless only four uniquetaggants are used, because this strategy provides no information on theinner portions of the taggants. Multiple PCR reactions must be run toobtain this information; how to accomplish this in a systematic and costeffective manner that simultaneously allows for layered taggant decodingis a problem which, to the best of the Applicant's knowledge, has notbeen solved.

TABLE 2Taggant library TAG(5,2,50) created from table-mers of DNA_TC(5,2,10)of Table 1. numeric SEQ ID sequence NO: position 0 position 1 position 2position 3 position 4 00000 14 CGTCCATCGT CATTCGCGGA ACAGTTGCCGTCGGTAAGCG GAGCGAACCA 10000 15 GCAGAAGCCA CATTCGCGGA ACAGTTGCCGTCGGTAAGCG GAGCGAACCA 01000 16 CGTCCATCGT CGCAAGCTGA ACAGTTGCCGTCGGTAAGCG GAGCGAACCA 11000 17 GCAGAAGCCA CGCAAGCTGA ACAGTTGCCGTCGGTAAGCG GAGCGAACCA 00100 18 CGTCCATCGT CATTCGCGGA AGTGGATGCGTCGGTAAGCG GAGCGAACCA 10100 19 GCAGAAGCCA CATTCGCGGA AGTGGATGCGTCGGTAAGCG GAGCGAACCA 01100 20 CGTCCATCGT CGCAAGCTGA AGTGGATGCGTCGGTAAGCG GAGCGAACCA 11100 21 GCAGAAGCCA CGCAAGCTGA AGTGGATGCGTCGGTAAGCG GAGCGAACCA 00010 22 CGTCCATCGT CATTCGCGGA ACAGTTGCCGTGCACGAGAC GAGCGAACCA 10010 23 GCAGAAGCCA CATTCGCGGA ACAGTTGCCGTGCACGAGAC GAGCGAACCA 01010 24 CGTCCATCGT CGCAAGCTGA ACAGTTGCCGTGCACGAGAC GAGCGAACCA 11010 25 GCAGAAGCCA CGCAAGCTGA ACAGTTGCCGTGCACGAGAC GAGCGAACCA 00110 26 CGTCCATCGT CATTCGCGGA AGTGGATGCGTGCACGAGAC GAGCGAACCA 10110 27 GCAGAAGCCA CATTCGCGGA AGTGGATGCGTGCACGAGAC GAGCGAACCA 01110 28 CGTCCATCGT CGCAAGCTGA AGTGGATGCGTGCACGAGAC GAGCGAACCA 11110 29 GCAGAAGCCA CGCAAGCTGA AGTGGATGCGTGCACGAGAC GAGCGAACCA 00001 30 CGTCCATCGT CATTCGCGGA ACAGTTGCCGTCGGTAAGCG TCGGAGTGCT 10001 31 GCAGAAGCCA CATTCGCGGA ACAGTTGCCGTCGGTAAGCG TCGGAGTGCT 01001 32 CGTCCATCGT CGCAAGCTGA ACAGTTGCCGTCGGTAAGCG TCGGAGTGCT 11001 33 GCAGAAGCCA CGCAAGCTGA ACAGTTGCCGTCGGTAAGCG TCGGAGTGCT 00101 34 CGTCCATCGT CATTCGCGGA AGTGGATGCGTCGGTAAGCG TCGGAGTGCT 10101 35 GCAGAAGCCA CATTCGCGGA AGTGGATGCGTCGGTAAGCG TCGGAGTGCT 01101 11 CGTCCATCGT CGCAAGCTGA AGTGGATGCGTCGGTAAGCG TCGGAGTGCT 11101 36 GCAGAAGCCA CGCAAGCTGA AGTGGATGCGTCGGTAAGCG TCGGAGTGCT 00011 37 CGTCCATCGT CATTCGCGGA ACAGTTGCCGTGCACGAGAC TCGGAGTGCT 10011 38 GCAGAAGCCA CATTCGCGGA ACAGTTGCCGTGCACGAGAC TCGGAGTGCT 01011 39 CGTCCATCGT CGCAAGCTGA ACAGTTGCCGTGCACGAGAC TCGGAGTGCT 11011 40 GCAGAAGCCA CGCAAGCTGA ACAGTTGCCGTGCACGAGAC TCGGAGTGCT 00111 41 CGTCCATCGT CATTCGCGGA AGTGGATGCGTGCACGAGAC TCGGAGTGCT 10111 42 GCAGAAGCCA CATTCGCGGA AGTGGATGCGTGCACGAGAC TCGGAGTGCT 01111 43 CGTCCATCGT CGCAAGCTGA AGTGGATGCGTGCACGAGAC TCGGAGTGCT 11111 44 GCAGAAGCCA CGCAAGCTGA AGTGGATGCGTGCACGAGAC TCGGAGTGCT

Now consider an example of a larger taggant library which is made up oftable-mers having a sufficient number of nucleotides to ensure reliablePCR results, a larger bit depth, and a larger choice of values in thebits. Such an exemplary taggant library could be created as describedpreviously herein from a 3×10 table, DNA_TC(7,3,20), wherein q=3, n=7,and t=20. Such a table (not shown) consists of 21 table-mers havinglengths of 20 nucleotides, which can be concatenated to produce ataggant library of 3⁷ (2187) distinct single strands of DNA havinglengths of 140 nucleotides. This library may represent the 2187 numbersequence from 0000000 to 2222222. (For use as taggants, the 2187 ssDNAstrands would be converted to dsDNA WC duplexes so that the PCRtechnique could be used in taggant detection.)

A taggant library of this size is needed for many applications; forother applications, the size of the taggant library may be even greater.Nonetheless, there are severe problems in producing a taggant library ofthis size, with the taggants having such long nucleotide sequences.Firstly, there is an error rate in synthesizing any DNA sequence. Thelonger the sequence is, the greater the cumulative errors in thenucleotide sequence become, to the point where the nucleotide sequenceis not sufficiently accurate to enable the DNA strand to reliably serveas a taggant. Secondly, there is a yield loss rate per nucleotide added,such that the longer the sequence, the disproportionately greater thecost. Thirdly, the overall cost of synthesizing a library of over twothousand taggants would likely be prohibitive for the vast majority ofapplications. Fourthly, the logistics of precisely managing a library ofover two thousand taggants in the environment of their use would bedaunting and likely subject to an unacceptable error rate.

In summary, small taggant libraries of taggants having relatively shortsequences are of limited use in practical applications, andsubstantially larger desirable taggant libraries having longer sequencesneeded for bit depth (information content) are extremely difficult tosynthesize and are cost-prohibitive. What is needed are:

i. A relatively small number of sufficiently short DNA taggants that canbe provided cost-effectively.

ii. Methods of combining subsets of these sufficiently short DNAtaggants to convey the desired large amount of information for aparticular application.

iii. Methods of designing sufficiently short DNA taggants that can bemixed together to avoid PCR errors.

iv. Methods of analyzing the resulting data so that the informationcontained in a large number of DNA taggants can be decoded andunderstood with certainty.

DNA Taggants Defined Using Principles of Combinatorial Mathematics

In accordance with the invention, the problem of providing DNA taggantsthat are sufficiently short to be low in cost, while still individuallyencoding large amounts of information and collectively forming asufficiently large library of taggant choices is solved by providing DNAtaggants in which the nucleotide sequences are defined according toprinciples of combinatorial mathematics.

The PCR technique previously described herein may be used advantageouslyin the methods of the present invention. In certain embodiments, byincubating a DNA taggant mixture with oligonucleotide recognition sitePCR primers and the enzyme DNA polymerase, the presence of a pair ofrecognition sites on a common substrand of a DNA taggant can bedetermined by whether or not a PCR amplification occurs. This PCRamplification information can be mathematically exploited to detectindividual taggants and to detect and decode layered taggants.

In one aspect of the invention, by using smaller DNA fragments thatmathematically constitute what is known as a combinatorial cover (hencethe name ComDTag), the Applicant's method of defining a set ofcombinatorial DNA taggants and related method of using such taggants canprovide the same information that would be obtained from using a singlelonger DNA taggant that is prepared in accordance with prior artmethods.

FIG. 2 is a flowchart depicting one embodiment of the Applicant's methodof defining a set of combinatorial DNA taggants and using such taggants.The method 100 comprises defining 110 a table of table-mer nucleotidesequences that can be used to construct a library of DNA taggants,creating 120 the library of taggants, and performing a combinatorialanalysis 135 of the table-mer sequences to determine the covering DNAstrands needed to simulate the taggants of the library. Thecombinatorial analysis 135 may be performed by building 130 a networkgraph of possible PCR reactions from primer pairs of table-mers, andanalyzing 140 the network graph to determine the DNA covering strands.It will be seen that the covering DNA strands are much shorter than theDNA taggants of the taggant library, and the number of covering strandsneeded to simulate all of the DNA taggants of the taggant library ismuch less than the number of taggants in the library. Thus the instantcombinatorial DNA taggants are sufficiently short to be low in cost,while still being capable of encoding large amounts of information andcollectively forming a sufficiently large library of taggant choices.

The method 100 will now be explained using the table-mers of the tablecode DNA_TC(5,2,10) of Table 1, and the associated taggant libraryTAG(5,2,50) of Table 2. As recited previously, this taggant library islikely to be unsuitable for practical uses; however, because of itssimplicity, it is used here for illustrative purposes. Examples of alarger taggant library and its combinatorial cover will be presentedsubsequently.

It is first noted that for a general taggant library TAG(n,q,nt), thereare n(n−1)q²/2 primer pairs of table-mers. Therefore, there are the samenumber of distinct PCR reactions, with each taggant being positive forexactly n(n−1)/2 of them. Accordingly, for the table-mers of Table 1 andall 32 distinct taggants in TAG(5,2,50) formed therefrom and shown inTable 2, n=5 and q=2, so there are 40 distinct PCR reactions which canbe performed. Additionally, any given taggant is positive for ten of thePCR reactions.

FIG. 3A depicts a network graph 200 that may be used in defining the DNAcovering strands for the taggant library of Table 2. In the networkgraph 200, the ten table-mers 210 of Table 1 are arrayed as a set ofnodes in a roughly circular manner. The lines 220 connecting the nodes210 in the graph 200 denote all possible primer pairs of thesetable-mers. It is noted that there are no lines between primer pairswith the same first coordinate (such as e.g., (4,0) and (4,1)). This isbecause no single taggant can have two distinct table-mers at the sameposition. There are 40 lines 220 (also known as edges in network graphanalysis) in FIG. 3A, which show the 40 distinct PCR reactions which canbe performed.

FIG. 3B depicts the network graph of FIG. 3A, modified to identify theset of positive PCR reactions for the DNA taggant of Table 2 that isrepresented by the value 01101. The set of bold lines 222 denotes theset of positive PCR reactions for the DNA taggant represented by 01101.As noted previously, the taggant represented by the numerical value01101 (SEQ ID NO: 11) is

CGTCCATCGT CGCAAGCTGA AGTGGATGCG TCGGTAAGCG TCGGAGTGCT.   (0,0)      (1,1)      (2,1)      (3,0)      (4,1)

For clarity in correlating the above with FIG. 3B, the respectiveordered pairs of the individual digits are also shown. It can be seen inFIG. 3B that bold lines are shown between the following table-mers:(0,0)↔(1,1); (0,0)↔(2,1); (0,0)↔(3,0); (0,0)↔(4,1); (1,1)↔(2,1);(1,1)↔(3,0); (1,1)↔(4,1); (2,1)↔(3,0); (2,1)↔(4,1); and (3,0)↔(4,1).

In practicing the PCR method, if the series of all 40 possible PCRreactions shown in FIG. 3A were run one by one, and amplification (i.e.,the PCR “signal”) were observed in the above ten PCR reactions, thatwould indicate that the taggant represented by the numerical value 01101was present in the sample being analyzed. However, having to providesuch a taggant library of DNA taggants having long nucleotide sequencesis disadvantageous for the reasons noted previously, particularly whenthe number of nucleotides exceeds about 100, and the need for extensiveencoded information causes the library to become large.

In addressing this problem, the Applicant has discovered that by usingsmaller DNA fragments that mathematically constitute what is known as acombinatorial cover, the same PCR network graph information can beobtained as would be provided by using a longer DNA taggant. Tounderstand this discovery, consider the set M as being a fixedcollection of table-mers DNA_TC(n,q,t). An s-DNA combinatorial cover ofM is a collection of double-stranded WC duplex concatenations of stable-mers taken from M that yield exactly all the same positive PCRreactions that exist for the entire taggant library TAG(n,q,nt) for M. ADNA sequence in an s-DNA cover is called a “covering strand” in thisdisclosure. Additionally, since the length of such a covering strand iss·t base pairs, the s-DNA cover of M is denoted herein as aCOV_DNA(n,q,st) of M. COV_DNA(n,q,st) of M may also be referred to as ans-DNA cover of the taggant library TAG(n,q,nt) constructed from M.

By using DNA combinatorial covers of idealized DNA taggant libraries,“virtual taggants,” also known herein as ComDTags, can be constructed.These combinatorial DNA taggants behave exactly like longer taggants inthe library with respect to their PCR signal. (Thus the ComDTags are“virtual” in the sense that they simulate longer idealized taggants ofthe taggant library.) Thus, for TAG(n,q,nt), instead of having topainstakingly construct q^(n) taggants, and having the problems of highcost and low yield, one can construct approximately q^(s) strands inCOV_DNA(n,q,st). The same results as when using a taggant from thelibrary can be obtained by algorithmic mixing to make the ComDTags. Thismethod provides a reduction in taggant cost on the order of q^(n-s). Forexample, with n=10, q=2, s=3, the reduction is 2¹⁰⁻³, i.e.,approximately 100 fold. Moreover, the physical construction of long DNAtaggant sequences when n·t is greater than 200 is cost prohibitive, andvirtually impossible if n·t is greater than 250. Thus, to get massiveamounts of data storage capabilities, the combinatorial coverCOV_DNA(n,q,st) must be used.

Continuing with the use of the TAG(5,2,50) of Table 2 constructed fromthe table-mers of Table 1 as an example, let C be a COV_DNA(5,2,30)3-cover. The four covering strands cs₁, cs₂, cs₃ and cs₄ in C thatappear below in Table 3 together constitute a virtual ComDTag taggantfor the actual taggant that appears in FIG. 1, which is the taggantrepresenting the numerical value 01101. The table-mers (shown in Table 3with their respective ordered pair references) which form the coveringstrands of Table 3 have been selected according to the principles ofcombinatorial mathematics, specifically to provide the same PCR signalresponse as the full length five bit taggant of FIG. 1. The use of thiscombinatorial DNA taggant in lieu of the taggant of FIG. 1 will now beexplained in detail, using a hypothetical example, with reference alsoto FIG. 2.

TABLE 3Covering strands for the DNA taggant of FIG. 1, a COV_DNA(5,2,30)3-cover shown as WC duplexes.            (0,0)      (1,1)      (2,1)(SEQ ID NO: 45) cs₁ = 5’CGTCCATCGT CGCAAGCTGA AGTGGATGCG3’      3’GCAGGTAGCA GCGTTCGACT TCACCTACGC5’            

           (0,0)      (1,1)      (4,1) (SEQ ID NO: 46) cs₂ =5’CGTCCATCGT CGCAAGCTGA TCGGAGTGCT3’      3’GCAGGTAGCA GCGTTCGACT AGCCTCACGA5’            

           (2,1)      (3,0)      (4,1) (SEQ ID NO: 47) cs₃ =5’AGTGGATGCG TCGGTAAGCG TCGGAGTGCT3’      3’TCACCTACGC AGCCATTCGC AGCCTCACGA5’                

           (0,0)      (1,1)      (3,0) (SEQ ID NO: 48) cs₄ =5’CGTCCATCGT CGCAAGCTGA TCGGTAAGCG3’      3’GCAGGTAGCA GCGTTCGACT AGCCATTCGC5’                

Referring to FIG. 2, a set of ComDTags, which may include the ComDTag ofTable 3, is prepared according to steps 110-150. Now suppose a targetobject A is tagged in step 160 with the ComDTag of Table 3, i.e. thefour covering strands cs₁-cs₄ as an indication of authenticity. Object Ais later recovered in step 170, and undergoes whatever routine procedureis required to extract any DNA taggant (if present) therefrom, and toplace the DNA taggant in solution so that it can be tested using the PCRtechnique, which is performed in step 180.

The only PCR reactions that need to be run to detect the presence of thefour covering strands are those reactions between the five table-mersthat make up those strands, i.e., (0,0), (1,1), (2,1), (3,0), and (4,1),with those five table-mers being used are primers for the PCR. (However,the remaining PCR reactions may need to be run to verify that no otherDNA taggants from library are present in applications where multipleproducts have been labeled by multiple taggants.) The “virtual” aspectof the collection of the four covering strands can be observed in FIG.4. Each of the four covering strands gives rise to three positive PCRreactions; so when the PCR technique is used, if the four coveringstrands are present (as would be the case when testing an authenticobject A above), those reactions will occur.

For example, cs₃ has positive PCR reactions for the primer pairs in thetriangle (2,1), (3,0), (4,1), the lines of which are marked with theshorter dashes (

). More specifically, when a PCR reaction is run with the primer pair(2,1) and (3,0), the left two bits of cs₃ consisting of (2,1)(3,0) willbe amplified. When a PCR reaction is run with the primer pair (3,0) and(4,1), the right two bits of cs₃ consisting of (3,0)(4,1) will beamplified. When a PCR reaction is run with the primer pair (2,1) and(4,1), the entire cs₃ strand will be amplified. In all cases, these PCRreactions produce amplification, i.e. increased DNA concentrations thatcan be detected by the aforementioned known analytical methods. It canbe seen that it is not necessary to the PCR reactions reproduce theentire cover strand for them to provide meaningful data.

In like manner, cs₁ has positive PCR reactions for the primer pairs inthe triangle (0,0), (1,1), (2,1), the lines of which are shaded withcircular dots; cs₂ has positive PCR reactions for the primer pairs inthe triangle (0,0), (1,1), (4,1), the lines of which are shaded withsquare dots; and cs₄ has positive PCR reactions for the primer pairs inthe triangle (0,0), (1,1), (3,0), the lines of which are shaded with thelonger dashes. (It is noted that the line between the primers (0,0) and(1,1) appears in three of the four triangles, and is thus partiallyhighlighted by three different markings.)

Comparing FIG. 4 to FIG. 3B, it can be observed that cs₁, cs₂, cs₃ andcs₄ in total give the same ten distinct positive PCR reactions as doesthe single longer taggant 10 of FIG. 1 that they cover. Thisadvantageous result is from the Applicant's use of combinatorialmathematics to design the cover strands. In designing the coveringstrands, first the table-mers present in a given idealized taggant thatis to be simulated by the collection of cover strands that make theactual ComDTag are identified. Referring again to FIGS. 1 and 3B as anexample, the five table-mers 224 of the taggant 10 are identified. Thepositive PCR reactions 222 between them are then identified using thenetwork graph 200. The minimum number of cover strands are thenidentified, such that the combinations of table-mers in those coverstrands will cover all of the required PCR reactions. Referring to Table3 and FIG. 4, it can be seen that the table-mers in the cover strandsare chosen such that all the desired PCR reactions that would occur inthe full length idealized taggant are covered. In other words, coverstrand cs₁ contains the table-mers of bits 0, 1, and 2; cover strand cs₂contains the table-mers of bits 2, 3, and 4; cover strand cs₃ containsthe table-mers of bits 0, 1, and 4; and cover strand cs₄ contains thetable-mers of bits 0, 1, and 3. Accordingly, all of the PCR reactionsthat occur between the table-mer primers of all bit pairs, i.e., 0-1,0-2, 0-3, 0-4, 1-2, 1-3, 1-4, 2-3, 2-4, and 3-4 are covered.

From the perspective of the positive PCR reactions, the single longeridealized taggant 10 of FIG. 1 is indistinguishable from the mixture ofthe covering strands of Table 3, i.e., the taggant ComDTag. It is muchmore feasible and cost effective to synthesize four relatively shortcover strands than it is to synthesize the single longer taggant strand.It is noted again that for illustrative purposes, the above example usesa shorter taggant, concatenated from shorter table-mers than would bedesired for practical applications. Thus the Applicant's method becomeseven more enabling and cost effective when longer taggant strands andlonger table-mers are used as required in many practical applications.

Additionally, it is not necessary that every taggant in a library has aunique set of covering strands, such that a given taggant libraryrequires the synthesis of covering strands of many times its population.With the covering strands being designed according to combinatorialmathematics, there is overlap in covering strands between taggants. Inother words, a single covering strand is used to (partially) cover manydifferent idealized and longer taggants. For example cs₁ (partially)covers all idealized taggants corresponding to the bit strings 011xx.For example, the 32 taggants of the library TAG(5,2,50) of Table 2requires only a total of 32 covering strands, so in this instance thereis just a reduction in the length of the strands and not the number ofstrands. However for the 2187 idealized DNA taggants of length 140constructed from DNA_TC(7,3,20), wherein q=3, n=7, and t=20, only 187covering strands, each of length 60 base pairs, need to be produced.

The Applicant's combinatorial DNA taggants, and related methods may beextended to the use of layered taggants. FIG. 5 is a network graph 240of positive PCR reactions for the group 11000, 00110, 11100 and 11110 offour layered taggants selected from the taggant library TAG(5,2,50) ofTable 2. It is noted that theoretically, FIG. 5 would appear the sameregardless of whether the four actual TAG(5,2,50) sequences 11000,00110, 11100 and 11110 of 50 base pairs, or the sixteen (with somerepetition possible) covering strands of 30 base pairs inCOV_DNA(5,2,30) that covered each of the taggants 11000, 00110, 11100and 11110, were combined. The covering strands for 11000, 00110, 11100and 11110 are respectively:

{(012)(110), (034)(100), (134)(100), (234)(000)} {(012)(110),(034)(010), (134)(110), (234)(110)} {(012)(111), (034)(100), (134)(100),(234)(100)} {(012)(111), (034)(110), (134)(110), (234)(110)}

So in total there are 11 distinct covering strands (e.g., (012)(111) and(134)(110) are among repeated strands) for the layer collection of11000, 00110, 11100,11110. Hence if these taggants were layeredsimultaneously, there would be an additional reduction in number ofcovering strands needed to construct the virtual taggant layering.However, if taggants are layered in series over time, there areapplications where some covering strands would be necessarily repeated.For example, different ingredients in a drug might have some (not all)similar covering strands and then, when combined as a single drug,similar covering strands would be repeated in the resulting layeredtaggant for the drug.

As a further demonstration of certain aspects of the invention, a morecomplex example of the combinatorial DNA taggants and related methodswill now be presented. Table 4 is another exemplary table having threevalues by five positions, and designated DNA_TC(5,2,26), with thetable-mers being 26 nucleotides long.

TABLE 4Exemplary table according to table code DNA_TC(5,3,26). All sequences are 26nucleotides (SEQ ID NOS 49-63, respectively, in order of appearance), readleft-to-right and top-to-bottom. VALUE position 0 position 1 position 2position 3 position 4 0 TCAACTCTTACCT ATCTTCTCCTCCA CTCTCACTCTCTCTTCCTACCAAAAC ATCATCCACTATC CAATCTCATACCA ATCCATTTCTCAT ACTCCTTATCAATCAAAAACTCCAAT CTCTACAACACTT 1 AACAACCATTCTC CATCCTTCTTTCA TTTCCAATTCCAAAAATCCACCTTTT CAAAACAAACACT CAACCTTCATATT CTTACACTCACAT CATAATCCACACACACAAAACTACCT CAACTACACTCTC 2 TCAAATCACTACC ACACACACAACA ACTCACACCAATAAACCCTCCTAATCA TTCACCTCTCTTC ATCTTTTCCACAA ACACCAAAAATAAA TCTACTTTCTCCTCCTCCTATTACAC CTAAATTCCTCTT

TABLE 5 Covering strands for the DNA taggant represented by 01121,a COV_DNA(5,3,78) 3-cover. All sequences are 26nucleotides (SEQ ID NOS 49, 62, 58, 56, 62, 58, 49, 55, 56,55, 62, and 58, respectively, in order of appearance),read left-to-right and top-to-bottom. (01234)(01211) (034)(021)TCAACTCTTACCT AACCTCCTAATCA CAAAACAAACACT CAATCTCATACCA CCTCCTATTACACCAACTACACTCTC (234)(121) TTTCCAATTCCAA AACCTCCTAATCA CAAAACAAACACTCATAATCCACACA CCTCCTATTACAC CAACTACACTCTC (012)(011) TCAACTCTTACCTCATCCTTCTTTCA TTTCCAATTCCAA CAATCTCATACCA CTTACACTCACAT CATAATCCACACA(134)(121) CATCCTTCTTTCA AACCTCCTAATCA CAAAACAAACACT CTTACACTCACATCCTCCTATTACAC CAACTACACTCTC

From the table-mers in Table 4, a taggant library TAG(5,3,130) (notshown) may be created having 3⁵=243 distinct taggants. As notedpreviously, for a general taggant library TAG(n,q,n·t), there aren(n−1)q²/2 primer pairs of table-mers, and thus the same number ofdistinct PCR reactions with each taggant being positive for n(n−1)/2 ofthem. In this instance, n=5 and q=3, so there are 90 distinct PCRreactions to perform with any given taggant being positive for 10 ofthem. Although ninety reactions may appear to be a substantial number,current real time PCR technology, such as that of the aforementionedStratagene 3000 MX Pro PCR apparatus enables the performance of up to 96simultaneous reactions.

A network graph may be constructed as described previously. FIG. 6A isthe network graph depicting the fifteen table-mers 260 of Table 4 andthe 90 distinct PCR reactions 270. Referring also to FIG. 6B, the set ofbold lines 272 denotes the set of positive PCR reactions for the DNAtaggant

(SEQ ID NO: 64) TCAACTCTTACCTCAATCTCATACCA CATCCTTCTTTCACTTACACTCACATTTTCCAATTCCAACATAATCCACACA AACCTCCTAATCACCTCCTATTACACCAAAACAAACACTCAACTACACTCTC represented by 01121. (In graph theoretical terms, this collection ofbold edges is called a n-clique (5-clique here), because all of the fivevertices (5) involved are mutually connected.)

As described previously, a combinatorial cover may be constructed forthe taggant library TAG(5,3,130). Let C be a COV_DNA(5,3,78) 3-cover forthis library. The four covering strands (034)(021), (234)(121),(012)(011), (134)(121) in C that appear in Table 5 together constitute avirtual ComDTag taggant for the above actual taggant from the taggantlibrary TAG(5,3,130). The encoding method (position string)(valuestring) relative to a given table is used to encode the identity of astrand. For example (034)(021) is the concatenation of strands (0,0),(3,2) and (4,1). For consistency, (01234)(01121) denotes the collectionof strands in Table 2, i.e., the virtual ComDTag for 01121.

As described previously, the “virtual” aspect of the collection of thefour covering strands can be observed in Table 5. Each of the fourcovering strands gives rise to three positive PCR reactions. Forexample, (012)(011) has positive PCR reactions for the primer pairs inthe triangle (0,0), (1,1), (2,1) whose lines are solid black. Thetriangle of edges that are positive for each covering strand (round dotsrespectively. It is noted that the line between (3,2) and (4,1) appearsin three of the four triangles and is thus partially highlighted bythree different line formats. Comparing FIG. 7 to FIG. 6B, it can beobserved that (034)(021), (234)(121), (134)(121) and (012)(011) in totalgive the same ten positive PCR reactions as does the single longertaggant that they cover.

In a graphical representation of PCR reactions, only the edges thatdenote positive PCR reactions need to be shown. The modified networkgraph 255 of FIG. 8 gives the positive PCR reactions for the group offour layered ComDTags (01234)(11111), (01234)(01222), (01234)(01121),(01234)(10101) consisting of 16 ComDTag fragments. It has beenexperimentally verified that FIG. 8 is the same regardless of whetherthe four actual TAG_LIB(5,3,130) sequences 11111, 01222, 01121, 10101 of130 base pairs, or the sixteen ComDTag fragment covering strands of 78base pairs were used in the PCR technique.

Laboratory Demonstration of Combinatorial DNA Taggants and Methods

Proof of principle of the instant DNA taggants and method has beensuccessfully performed, as disclosed in “PCR Nonadaptive Group Testingof DNA Libraries for Biomolecular Computing and Taggant Applications,”Discrete Mathematics, Algorithms and Applications, Vol. 1, Issue 1(March2009), 59-69, Macula, et al. In the study, a set of combinatorial DNAtags was designed and synthesized. A mixture of a small subset of thetaggants was prepared and analyzed with the PCR technique as describedherein. The laboratory mixture simulated a mixture that could beprepared from a sample of a target that was tagged with the taggantmixture.

FIG. 9A is a gel electrophoresis image 300 of the combinatorial DNAtaggants that were amplified using the PCR method. The PCR data from theimage 300 of FIG. 10 was analyzed and interpreted mathematically as thenetwork graph 310 of FIG. 10. Mathematical methods were then used todecompose the graph 310 into components that represent each of thetaggants present, which are shown in FIG. 11. The mathematicaldecomposition methods correctly identified the four taggants of FIG. 10.This experiment simulated a complex real-world use of layered taggants,such as the output of a four step drug production protocol, i.e. usingfour layered taggants to track and trace a drug product and process.

To get usable layerable and decodable ComDTags, a computer generates theComDTags to be layered so that they can be decoded by the uniquen-clique method discussed below where n is the number of digit positionsin the idealized DNA taggant. The given unique n-clique decoding methodis a generalization of “edge representative decoding” that appears inthe publication of Hwang, F. K., Liu, Y. C., Random Pooling DesignsUnder Various Structures, Journal of Combinatorial Optimization 7,339-352, 2003.

Let the term positive PCR network graph as used herein denote thecollection of solely positive PCR reactions.

A standard computer search algorithm ensures that each n-cliquecorresponding to a given ComDTag in a layered collection of ComDTags hasat least one edge, E, in the positive PCR network graph such that E is amember of one and only one n-clique subgraph of the positive PCR networkgraph.

Note that every ComDTag always corresponds to a n-clique subgraph ofpositive PCR network graph, but not necessarily vice-versa. There can ben-clique subgraphs in the positive PCR network graph that do notcorrespond to a ComDTag in the layered collection of ComDTags that givesrise to the PCR signal represented by positive PCR network graph.

The unique n-clique method that is now described identifies then-cliques that do correspond to ComDTags.

The unique n-cliques method operates on positive PCR network graph bysearching over its edges for those contained in a unique n-clique. If anedge is a member of a unique n-clique in the PCR graph, then that uniquen-clique represents a ComDTag. Note, an n-clique may contain severalunique edges and this redundancy give the unique n-clique methodconsiderable experimental error-correcting capability.

Since only unique n-cliques are taken, unique n-clique algorithms nevermis-identify a non-ComDTag (in the absence of experimental error). Itshould be noted that since false positives experimental PCR errorintroduce more (but false) edges in the positive PCR network graph,these added (but false) edges can only increase the number of n-cliquespresent. Hence false positives cannot lead to the misidentification of aComDTag. False positives can cause some ComDTags not to be identified,but what partial information is obtained in the presence of falsepositive experimental error is still correct, albeit perhaps partial,decoding. This is a very attractive aspect of the Applicant's method, asfalse positives are more likely than false negatives in PCRapplications.

For example, recall from FIG. 3B and FIG. 4 that each ComDTag (in thatexample displayed) corresponds to a 5-clique in the PCR graph. FIG. 5 isthe positive PCR network graph signal received from a layered mixture ofthe four taggants (01234)(11000), (01234)(00110), (01234)(11100) and(01234)(11110) selected from the taggant library TAG(5,2,50) of Table 2.

Applying the unique 5-clique method to FIG. 5 gives that:

edge (0,1)↔(2,0) is unique for 5-clique (01234)(11000),edge (0,0)↔(1,0) is unique for 5-clique (01234)(00110),edge (2,1)↔(3,0) is unique for 5-clique (01234)(11100), andedge (0,1)↔(3,1) is unique for 5-clique (01234)(11110).

Thus all four of the layered taggants have been successfully decoded inthis case.

In the above experimental study, gel electrophoresis was used to providedata on the amplification of the DNA taggants. Other analyticaltechniques are also suitable, such as those previously identifiedherein. Such methods and instruments can reliably provide theinformation needed to perform the mathematical algorithms used in theinvention in a fast and cost effective manner.

Alternative and Exclusively Binary Combinatorial DNA Taggants and Method

In accordance with the invention, alternative combinatorial DNA taggantsand methods are provided. These taggants and methods will now bedescribed through the use of illustrative examples thereof.

In a second method of representing solely binary sequences in DNA, onemay begin with a fixed set of n relatively short t-mers of ssDNA andtheir reverse complements. An exemplary set is shown in Table 6 below,wherein n=4 and t=22.

In the general case of this method, a total of n(n−1)/2 concatenationsof the strands and their complements may be made. This enables theencoding of bit strings up to a length of n(n−1)/2. Table 7 depicts therelationship between the number of table strands and complements, thenumber of encoding bit register strands, and the number of distinct bitstrings that can be encoded using the table strands and their reversecomplements. For the strands of Table 6, six concatenations of thestrands are possible, as shown in Table 8.

TABLE 6Exemplary table of short single DNA strands (SEQ ID NOS 65-68, respectively, inorder of appearance) and their reverse complements (SEQ ID NOS 69-72, respectively,in order of appearance), all shown in 5′→3′ order. strand 1GCGTGATAGTTACTTAACGATC complement 1 GATCGTTAAGTAACTATCACGC strand 2ATCAACATTGCTATACTCACTG complement 2 CAGTGAGTATAGCAATGTTGAT strand 3TGTTCTGTACGAGCTAGATTAT complement 3 ATAATCTAGCTCGTACAGAACA strand 4CACATCATTCAACAATCTGAGA complement 4 TCTCAGATTGTTGAATGATGTG

TABLE 7 Relationship between number of table strands and complements,number of encoding bit register strands, and number of distinct bitstrings that can be encoded. n = number of N = number of B = number ofdistinct table strands and encoding bit register bit strings complementsof strands of length 2t that can be encoded length t N = n(n − 1)/2 B =2^(N) 2 1 2 4 6 64 6 15 32768 8 28 268435456 10 45 3.51844 × 10¹³ 15 1054.05648 × 10³¹ 20 190 1.56928 × 10⁵⁷

TABLE 8 Example of bit register encoding using ssDNA strands of Table 6.bit register encoding strands (concatenations of t-mers and complements)(SEQ ID NOS 73-78, respectively, in order of appearance) encoder bit   strand 1 t-mer        strand 2 reverse complement register 1GCGTGATAGTTACTTAACGATC CAGTGAGTATAGCAATGTTGAT encoder bit   strand 1 t-mer        strand 3 reverse complement register 2GCGTGATAGTTACTTAACGATC ATAATCTAGCTCGTACAGAACA encoder bit   strand 1 t-mer        strand 4 reverse complement register 3GCGTGATAGTTACTTAACGATC TCTCAGATTGTTGAATGATGTG encoder bit   strand 2 t-mer        strand 3 reverse complement register 4ATCAACATTGCTATACTCACTG ATAATCTAGCTCGTACAGAACA encoder bit   strand 2 t-mer        strand 4 reverse complement register 5ATCAACATTGCTATACTCACTG TCTCAGATTGTTGAATGATGTG encoder bit   strand 3 t-mer        strand 4 reverse complement register 6TGTTCTGTACGAGCTAGATTAT TCTCAGATTGTTGAATGATGTG

TABLE 9 Bit register readers to read encoding strands of Table 8. bitregister readers: corresponding unique positive primer pair reader bitStrand 1 Strand 2 register 1 reader bit Strand 1 Strand 3 register 2reader bit Strand 1 Strand 4 register 3 reader bit Strand 2 Strand 3register 4 reader bit Strand 2 Strand 4 register 5 reader bit Strand 3Strand 4 register 6

For the strands of Table 6, six concatenations of the strands arepossible, as shown in Table 8. It can be seen that by using this method,any binary sequence (bit string) of length six can be encoded (orwritten) by mixing corresponding encoding strands that correspondexclusively to the bit registers with value 1. Then, as shown by Table9, the encoded bit string can be can be decoded (or read) by exposingthe mixture to six PCR reactions. Each PCR reaction may be primed by theunique corresponding primer pairs, wherein the left primer may be thefirst part of the encoding strand and the right primer may be thecomplement of the second part of the encoding strand. (In this case, thePCR reaction occurs only at the right ends of the strands in solution inthe first PCR cycle; and in subsequent PCR cycles, the PCR reaction canoccur at both ends of the strands. It will be apparent thatalternatively, the primer pair may be chosen such that the left primermay be the complement of the first part of the encoding strand and theright primer may be the complement of the second part of the encodingstrand.) To facilitate the decoding/reading, the PCR reactions may bedye-based.

FIG. 12 depicts an example in which the bit string 101101 is encoded bymixing the concatenated strands of encoder bit register 1, encoder bitregister 3, encoder bit register 4, and encoder bit register 6 into asingle liquid solution. This is done according to the general principleof this method, which is that for each entry in the bit string, theparticular bit encoding concatenated strand is included in the solutionif and only if the value in the given entry is a 1. Thus for the bitstring 101101, the first, third, fourth, and sixth bits are 1's, andtherefore, the concatenated strands for encoder bit registers 1, 3, 4,and 6 of Table 8 are included in the solution. Conversely, the secondand fifth bits are 0's, and therefore, the concatenated strands forencoder bit registers 2 and 5 of Table 8 are absent from the solution.

Referring to FIG. 12, and in the method 400 depicted therein, the fourssDNA strands representing encoder bit registers 1, 3, 4, and 6 areplaced in a solution 405. The solution 405 is then divided into sixaliquots, or six samples are taken from the solution 405. PCR reactionsare then run, wherein the respective samples are reacted with eachprimer pair of register readers of Table 9. Since each register readingprimer pair will only react positively with its correspondingconcatenated encoder strand, any bit string can be encoded by simplymixing together all the encoding register strands that correspond to a 1in the bit string that is to be encoded. It can be seen from FIG. 12that positive PCR reactions (i.e. amplification) occurs where theencoder strands are present. As noted previously, the PCR reactions maybe dye-based, so that a positive reaction is indicated by a color changethat can be visually observed or optically read.

In accordance with the invention, the combination of strandsrepresenting a particular bit string may be used as a combinatorial DNAtaggant, or as a layered combinatorial DNA taggant. Using the strands ofTable 6 and Table 8, and the bit string 101101 again as an example, thesolution of FIG. 12 containing the encoder bit registers 1, 3, 4, and 6may be applied to a target object, or the ssDNA of encoder bit registers1, 3, 4, and 6 may be individually applied in or onto a target object.For a layered taggant, they may be applied at different points of amanufacturing process. Subsequently the target object may be recoveredwith a need for authentication and/or tracking and tracing. Some of thetaggant DNA may be recovered from the object, again placed in solution,divided into six samples, and the six respective PCR reactions run. If aresult as shown in FIG. 12 is obtained, authenticity and/or the propercomplete tracing through the process would be verified. This method ofconstruction of DNA taggants can be employed in all the aforementionedreal world applications, e.g., drugs. Moreover, with this binaryencoding, all classical and well established information-theoreticmethods of processing binary digital signals can be applied to theinterpretation of binary signals generated by the PCR methods describedabove. Thus individual taggants can be encoded and decoded via classicalerror-correcting methods, such as those disclosed in F. J. MacWilliamsand N. J. A. Sloane, The Theory of Error-Correcting Codes, ISBN:0-444-85193-3, 762 pp., North-Holland Mathematical Library, Volume 16.Publisher: North-Holland, New York, 1998. Additionally, layered taggantscan be encoded and encoded via superimposed and disjunct coding, usingmethods such as those disclosed in Du, D. Z. and Hwang, F. K., 2000.Combinatorial Group Testing and Its Applications, 2nd ed. WorldScientific, Singapore.

The above method is particularly suitable for use with dye-basereal-time qPCR detection methods. If a probe based PCR detection methodis used, a slightly different encoding method must be used incombination with it. Continuing to build on the previous examples, thessDNA strands of Table 8 and Table 9 may be augmented with a probe-probecomplement pair. Such a complement pair may be, e.g., probe:AAGAGTTGTCATTACTCGAATG (SEQ ID NO: 79) and probe complement:CATTCGAGTAATGACAACTCTT (SEQ ID NO: 80).

Table 10 and Table 11 present the respective bit register encoders andbit register readers for this example. It can be seen that the bitregister encoders of Table 10 each have the probe complement insertedbetween the respective t-mer and complement strands. Thus these bitencoders are concatenations of three strands. The t-mer and complementends of these new strands are exactly the same as for the example ofTable 8, and therefore are unique for exactly the same positive PCRreactions previously described. Accordingly, there are exactly the samenumber of bit encoding strands as before and exactly the same number ofdistinct bits strings can be encoded.

TABLE 10Example of bit register encoding using ssDNA strands of Table 6 foruse with probe-based PCR detection. bit register encoding strands(concatenations of t-mer strands and complements)(SEQ ID NOS 81-86, respectively, in order of appearance) encoder bit   strand 1 t-mer         probe complement    strand 2 reverse complementregister 1GCGTGATAGTTACTTAACGATC CATTCGAGTAATGACAACTCTT CAGTGAGTATAGCAATGTTGATencoder bit   strand 1 t-mer         probe complement    strand 3 reverse complementregister 2GCGTGATAGTTACTTAACGATC CATTCGAGTAATGACAACTCTT ATAATCTAGCTCGTACAGAACAencoder bit   strand 1 t-mer         probe complement    strand 4 reverse complementregister 3GCGTGATAGTTACTTAACGATC CATTCGAGTAATGACAACTCTT TCTCAGATTGTTGAATGATGTGencoder bit   strand 2 t-mer         probe complement    strand 3 reverse complementregister 4ATCAACATTGCTATACTCACTG CATTCGAGTAATGACAACTCTT ATAATCTAGCTCGTACAGAACAencoder bit   strand 2 t-mer         probe complement    strand 4 reverse complementregister 5ATCAACATTGCTATACTCACTG CATTCGAGTAATGACAACTCTT TCTCAGATTGTTGAATGATGTGencoder bit   strand 3 t-mer         probe complement    strand 4 reverse complementregister 6TGTTCTGTACGAGCTAGATTAT CATTCGAGTAATGACAACTCTT TCTCAGATTGTTGAATGATGTG

TABLE 11 Bit register readers to read encoding strands of Table 10.bit register readers: corresponding unique probe (all disclosedpositive primer pair as SEQ ID NO: 79) reader bit Strand 1 Strand 2AAGAGTTGTCATTACTCGAATG register 1 reader bit Strand 1 Strand 3AAGAGTTGTCATTACTCGAATG register 2 reader bit Strand 1 Strand 4AAGAGTTGTCATTACTCGAATG register 3 reader bit Strand 2 Strand 3AAGAGTTGTCATTACTCGAATG register 4 reader bit Strand 2 Strand 4AAGAGTTGTCATTACTCGAATG register 5 reader bit Strand 3 Strand 4AAGAGTTGTCATTACTCGAATG register 6

The difference between the two methods is in the method of PCRamplification detection, as illustrated in FIG. 13. In both the method400 of FIG. 12 and the method 450 of FIG. 13, the bit registers areencoded by the first portions 410 and last portions 420 of the strands.

In the method 400 of FIG. 12, the encoding strands are of length s equalto two times the length of the t-mers, i.e. 44 base pairs in thisexample. In the method 450 of FIG. 13, the encoding strands are of alength equal to three times (or more) the length of the t-mers, i.e., 66base pairs in this example.

In the method 400, the amount of increase in doubled stranded DNA thatresults from PCR amplification is detected by means of a dye, such ase.g., the SYBR Green I asymmetrical cyanine dye. Such dyes arenon-specific, and detect any dsDNA that results from amplification.

In the method 450, a probe specifically detects the amplification of theinserted probe sequence 430, which is also amplified. Thus primer-dimerformation (which may occur in the method 400) does not lead to falsereads. Moreover, more than one probe sequence 430 may be used. A uniqueprobe sequence 430 may be inserted into each register encoding sequence440. (In the method 450 of FIG. 13, a common probe sequence 430 wasinserted for simplicity of illustration.) Thus this method of detectionis highly specific and less prone to error, albeit more expensive due tothe need to synthesize longer strands.

As recited previously for the strands of the method 400 of FIG. 12, thecombination of the n strands in the method 450 that represent aparticular bit string may be used as a combinatorial DNA taggant.

This method of construction of a DNA taggant in 400 and 450 is similarto the ComDTag method discussed above in 100 in that short strands arecombined to convey a long signal or sequence. However, methods 400 and450 are different from method 100 in the way the strands are combined.In methods 400 and 450, each strand in the combination represents adistinct bit register in a longer sequence that has value 1. The strandsnot in the given combination represent bit registers in a longersequence with value 0. The method in 100 encodes all q-ary values (0 toq−1) only with the presence of a shorter covering strand (i.e., itdoesn't use strand absence to denote a register value). Moreover, method100 is q-ary and encodes multiple q-ary registers on a single shortstrand. Methods 400 and 450 are exclusively binary and each strandencodes only one binary register.

Non-DNA Taggants Layered with Covert Combinatorial DNA Taggants

In accordance with the invention, the Applicant's combinatorial DNAtaggants may be layered with other non-DNA taggants. The non-DNAtaggants may be covert or overt taggants. The non-DNA taggants may be inliquid form, or solid form, such as a powder. In certain embodiments,the solid form taggant may be an up-converting phosphor material, whichwhen irradiated with energy of a specific wavelength, absorbs the energyand re-emits it at a different wavelength. The up-converting phosphormaterial may emit visible light when excited by long wavelength light.For example, ytterbium/erbium co-doped fluoride is a high efficiencyup-converting phosphor that emits strong green fluorescence andrelatively weak red fluorescence when excited by 946-970 nm infraredlight. Due to their unique properties, up-converting phosphors are usedin the fabrication of light-emitting diodes, solid-state lasers, and asultra-sensitive fluorescent labels in biological detections, such asthose disclosed in U.S. Pat. No. 5,674,698, the disclosure of which isincorporated herein by reference.

The Applicant's combinatorial DNA taggants may be blended with anup-converting phosphor material, which may be provided in powder form.One suitable up-converting phosphor material is MicroTagg™, which ismanufactured and sold by BrandWatch Technologies of Portland, Oreg. TheComDTags of method 100, 400 or 450 may be in a liquid solution, suchthat the liquid solution is combined with the up-converting phosphorpowder, with the resulting mixture then being dried. An attrition stepmay be performed if needed to reduce the resulting solid back toflowable powder form.

A taggant comprising one or more of the instant combinatorial DNAtaggants and an up-converting phosphor taggant is referred to herein asa phosphorDNA taggant. Such a taggant may be useful as a combinationovert-covert taggant. For example, when used, an initial detectionand/or authentication may be performed on the overt taggant, i.e. thephosphor powder, which is present on a target object. When irradiatedwith a particular wavelength, the emitting wavelength is detected,providing an initial fast indication of authenticity. Subsequently, thetarget object may be further analyzed, wherein the part of the objectcontaining the phosphorDNA taggant is recovered, and at least some ofthe combinatorial DNA taggant (if present) is placed in solution. ThePCR reactions and analysis as described herein are then run, and furtherdeterminations of authenticity and tracking and tracing are performed.

Any of the instant combinatorial DNA taggants disclosed herein may beused as layered taggants with a non-DNA taggant, such as anup-converting phosphor. The combinatorial DNA taggants may be madeaccording to the method 100 of FIG. 2, or made as described previouslyfor detection and analysis by the methods 400 and 450 of FIGS. 12 and13, respectively. For example, using the strands of Table 6 and Table 8,and the bit string 101101 again as an example, the strands of theencoder bit registers 1, 3, 4, and 6 of Table 8 may be mixed with anup-converting inorganic phosphor to produce a specific phosphorDNAtaggant.

If a particular ComDTag name used in a phosphorDNA is provided, thisspecific phosphorDNA may be referred to as phosphorDNA<fragmentname(s)>. For example, if ComDTag fragment, encoder bit register 1,abbreviated EBR1, from Table 8 has been used, then it may be referred toas phosphorDNA_EBR1. If a set S of multiple strands, e.g., all four ofthe fragments use to encode 101101 as described previously, i.e., EBR1,EBR3, EBR4, and EBR6 are used as a layered ComDTag in a phosphorDNA, itmay be referred to as phosphorDNA_101101.

However, if each member of a set S of ComDTag fragments is individuallyused as a tag to create a set of distinct phosphorDNAs, then the set ofindividual phosphorDNAs may be referred to as S<phosphorDNA>. Forexample, {EBR1,EBR3,EBR4, EBR6}_phosphorDNA={phosphorDNA_EBR1,phosphorDNA_EBR3, phosphorDNA_EBR4, phosphorDNA_EBR6}.

Thus by mixing the four separate powders in{EBR1,EBR3,EBR4,EBR6}_phosphorDNA into a single powder calledMix_{EBR1,EBR3,EBR4,EBR6}_phosphorDNA, the mixed powder will beindistinguishable from phosphorDNA_101101 in its PCR reactions. Oneadvantage of this method of making the phosphorDNA taggant is that it issignificantly easier to dry m distinct DNA strands into m distinctphosphors and then mix the phosphors, as compared to mixing the strandsand then drying 2^(m) individual mixtures on phosphors.

This method is illustrated in FIG. 14 using the above numerical sequenceand phosphorDNA_1010101 as an example. The method 500 comprisessynthesizing 510 the desired combinatorial taggants 512 that representnumber values or bit registers, such as taggants 512 prepared accordingto methods 100, 400, or 450 described previously herein. Thecombinatorial DNA taggants 512 are then mixed 520 with a non-DNAtaggant. As shown in FIG. 14, the non-DNA taggant may be an upconvertingphosphor. Other non-DNA taggants are contemplated. Mixing 520 the bitregister/number value taggants 512 with a phosphor taggant 521 producesindividual phosphor DNA taggants 522.

These individual phosphorDNA taggants 522 may be blended 530 to producea Mix_phosphorDNA taggant 532, which may represent a numerical sequence,such as mixing to provide Mix_{EBR1, EBR3, EBR4, EBR6}phosphorDNArepresenting 101101 as recited in the above example and shown in FIG.14. The Mix_phosphorDNA taggant 532 may be further diluted 542 withphosphor taggant 521 to produce manufacturing scale quantities ofphosphorDNA taggant for use as a layered taggant. This layered taggantmay have a DNA concentration on the order of tenths of a part pertrillion, while still being detectable by the PCR methods recitedherein.

The above method has been verified experimentally with the ComDTag(01234)(01211) of Table 5. In an experiment, 40 milliliters of 4nanomolar aqueous ComDTag (01234)(00000) was added to 40 grams of theup-converting phosphor MicroTagg of BrandWatch Technologies. This wasfollowed by drying, which produced 40 grams of phosphorDNA containing0.1 nanomole per gram of the ComDTag (01234)(00000). This ComDTag wasdetected by the PCR method at that concentration, and also at a furtheraqueous dilution of 10⁻⁶. This latter concentration is on the order of0.25 parts per trillion. Thus the instant combinatorial DNA taggants areknown to be detectable at extremely low concentrations.

Taggant Design and Synthetic DNA Code (SynDCode) Software

The decoding accuracy of DNA taggants using the PCR method depends uponwhether or not so-called false priming sites exist in the taggants. Thepriming sites for the Applicant's method may be one or more of thetable-mers used to construct the taggants, depending upon how long thetable-mers are. False priming site sequences can arise if two or more ofthe table-mers are too similar, or if the taggant sequence regions thatoverlap the junctions where table-mers are concatenated are too similarto the original table sequences.

To prevent this problem from occurring, the Applicant uses synthetic DNAcode software, SynDCode, to design the set of table-mers in a giventable. SynDCode is a software tool developed by the Applicant to designsynthetic DNA sequences to be used in biologically based informationsystems. Details on the algorithms and use of SynDCode may be found inAir Force Research Laboratory's Final Technical ReportAFRL-RI-RS-TR-2007-288, January 2008, “Superimposed Code TheoreticAnalysis of DNA Codes and DNA Computing,” by A. Macula, the disclosureof which is incorporated herein by reference. Examples of the use ofSynDCode to generate DNA code sequences are disclosed in NaturalComputing, Vol. 8, Issue 2, 2009, “Successful preparation and analysisof a 5-site 2-variable DNA library,” of Gal et al. Additionaldescriptions of SynDCode methods and applications can also be found inthe following references:

-   Arkadii G. D'yachkov, Anthony J. Macula, Wendy K. Pogozelski,    Thomas E. Renz, Vyacheslav V. Rykov, David C. Torney: A Weighted    Insertion-Deletion Stacked Pair Thermodynamic Metric for DNA Codes.    DNA 2004: 90-103;-   Arkadii G. D'yachkov, Anthony J. Macula, Wendy K. Pogozelski,    Thomas E. Renz, Vyacheslav V. Rykov, David C. Torney: New t-Gap    Insertion-Deletion-Like Metrics for DNA Hybridization Thermodynamic    Modeling. Journal of Computational Biology 13(4): 866-881 (2006);-   Morgan A. Bishop, Arkadii G. D'yachkov, Anthony J. Macula, Thomas E.    Renz, Vyacheslav V. Rykov: Free Energy Gap and Statistical    Thermodynamic Fidelity of DNA Codes. Journal of Computational    Biology 14(8): 1088-1104 (2007); and-   Anthony J. Macula, Alexander Schliep, Morgan A. Bishop, Thomas E.    Renz: New, Improved, and Practical k-Stem Sequence Similarity    Measures for Probe Design. Journal of Computational Biology 15(5):    525-534 (2008).

To summarize, SynDCode enables the specification of thermodynamicdistance and dissimilarity of the nucleotides in a DNA sequence suchthat the synthetic table-mers (and their complements) do not createfalse priming sites. The table-mers in the tables provided herein weredesigned by SynDCode to be non-complementary and non-cross-hybridizingso that each position in a taggant library strand is extremely highlyspecific for a unique PCR primer. It is known that SynDCode providesnon-cross-hybridizing output via repeated experimental verification inthe laboratory.

It is, therefore, apparent that there has been provided, in accordancewith the present invention, combinatorial DNA taggants and methods ofmaking and using such taggants. Having thus described the basic conceptsof the invention, it will be apparent to those skilled in the art thatthe foregoing detailed disclosure is intended to be presented by way ofexample only, and is not limiting. Various alterations, improvements,and modifications will occur and are intended to those skilled in theart, though not expressly stated herein. These alterations,improvements, and modifications are intended to be suggested hereby, andare within the spirit and scope of the invention. Additionally, therecited order of processing elements or sequences, or the use ofnumbers, letters, or other designations therefore, is not intended tolimit the claimed methods to any order except as may be specified in theclaims.

1-56. (canceled)
 57. A combinatorial DNA taggant comprising a set ofn(n−1)/2 unique bit register encoding strands, wherein: the n(n−1)/2unique bit register encoding strands ES₁ through ES_(n(n-1)/2) arecomprised of a first single stranded DNA strand selected from a set ofunique single stranded DNA strand S₁ through S_(n-1), and a secondsingle stranded DNA strand selected from a set of unique reversecomplement strands CS₂ through CS_(n), of the unique single stranded DNAstrands S₁ through S_(n); and wherein: n−1 of the unique bit registerencoding strands ES₁ through ES_(n(n-1)/2) are comprised of the uniquesingle stranded DNA strand S₁ concatenated, respectively, with theunique reverse complement strands CS₂ through CS_(n), and for each ofthese concatenations, concatenated such that there are no nucleotidebases between the 3′ end of the respective unique single stranded DNAstrand and the 5′ end of the unique reverse complement strand; and theremainder of the unique bit register encoding strands are comprised ofeach of the remaining unique single stranded DNA strands S_(i) throughS_(n-1) concatenated, respectively, with the remaining unique reversecomplement strands CS_(i+1) through CS_(n), and for each of theseconcatenations, concatenated such that there are no nucleotide basesbetween the 3′ end of the respective remaining unique single strandedDNA strand and the 5′ end of the remaining unique reverse complementstrand; where i is a natural number having an initial value of 2 and nis a natural number having a value greater than
 2. 58. A combinatorialDNA taggant comprising a set of n(n−1)/2 unique bit register encodingstrands, wherein: the n(n−1)/2 unique bit register encoding strands ES₁through ES_(n(n-1)/2) are comprised of a first single stranded DNAstrand selected from a set of unique single stranded DNA strand S₁through S_(n-1), and a second single stranded DNA strand selected from aset of unique reverse complement strands CS₂ through CS_(n), of theunique single stranded DNA strands S₁ through S_(n): n−1 of the uniquebit register encoding strands ES₁ through ES_(n(n-1)/2) are comprised ofthe unique single stranded DNA strand S₁ concatenated, respectively,with the unique reverse complement strands CS₂ through CS_(n); and theremainder of the unique bit register encoding strands are comprised ofeach of the remaining unique single stranded DNA strands S_(i) throughS_(n-1) concatenated, respectively, with the remaining unique reversecomplement strands CS_(i+1) through CS_(n), where i is a natural numberhaving an initial value of 2 and n is a natural number having a valuegreater than
 2. 59. The combinatorial DNA taggant of claim 58, whereinfor the n−1 of the unique bit register encoding strands ES₁ throughES_(n(n-1)/2) and for the remainder of the unique bit register encodingstrands they are concatenated such that there are no nucleotide basesbetween the 3′ end of the respective unique single stranded DNA strandand the 5′ end of the unique reverse complement strand.
 60. Thecombinatorial DNA taggant of claim 58, wherein each of the n(n−1)/2 bitregister encoding strand molecules in the set are further comprised of aprobe single stranded DNA strand concatenated between each of then(n−1)/2 single stranded combinations of DNA table-mers and theirreverse complements and wherein: the n(n−1)/2 unique bit registerencoding strands ES₁ through ES_(n(n-1)/2) are comprised of a firstsingle stranded DNA strand selected from the set of unique singlestranded DNA strand S₁ through S_(n-1), the probe singled stranded DNAstrand, and a second single stranded DNA strand selected from a set ofunique reverse complement strands CS₂ through CS_(n), of the uniquesingle stranded DNA strands S₁ through S_(n-1); n−1 of the unique bitregister encoding strands ES₁ through ES_(n(n-1)/2) are comprised of theunique single stranded DNA strand S₁ concatenated with the probe singlestranded DNA strand, and respectively concatenated with the uniquereverse complement strands CS₂ through CS_(n), and for each of theseconcatenations, concatenated such that there are no nucleotide bases,other than the probe single stranded DNA strand, between the 3′ end ofthe respective unique single stranded DNA strand and the 5′ end of theunique reverse complement strand; and the remainder of the unique bitregister probe encoding strands are comprised of each of the remainingunique single stranded DNA strands S_(i) through S_(n-1) concatenatedwith the probe single stranded DNA strand respectively, and with theremaining unique reverse complement strands CS_(i+1) through CS_(n), andfor each of these concatenations, concatenated such that there are nonucleotide bases, other than the probe single stranded DNA strand,between the 3′ end of the respective remaining unique single strandedDNA strand and the 5′ end of the remaining unique reverse complementstrand; where i is a natural number having an initial value of 2 and nis a natural number having a value greater than
 2. 61. A combinatorialDNA taggant comprising a set of n(n−1)/2 unique bit register encodingstrands, wherein: the n(n−1)/2 unique bit register encoding strandsProbeES₁ through ProbeES_(n(n-1)/2) are comprised of a first singlestranded DNA strand selected from the set of unique single stranded DNAstrand S₁ through S_(n-1), the probe singled stranded DNA strand, and asecond single stranded DNA strand selected from a set of unique reversecomplement strands CS₂ through CS_(n), of the unique single stranded DNAstrands S₁ through S_(n-1); n−1 of the unique bit register encodingstrands ProbeES₁ through ProbeES_(n(n-1)/2) are comprised of the uniquesingle stranded DNA strand S₁ concatenated with the probe singlestranded DNA strand, and respectively concatenated with the uniquereverse complement strands CS₂ through CS_(n), and for each of theseconcatenations, concatenated such that there are no nucleotide bases,other than the probe single stranded DNA strand, between the 3′ end ofthe respective unique single stranded DNA strand and the 5′ end of theunique reverse complement strand; and the remainder of the unique bitregister probe encoding strands are comprised of each of the remainingunique single stranded DNA strands S_(i) through S_(n-1) concatenatedwith the probe single stranded DNA strand respectively, and with theremaining unique reverse complement strands CS_(i+1) through CS_(n), andfor each of these concatenations, concatenated such that there are nonucleotide bases, other than the probe single stranded DNA strand,between the 3′ end of the respective remaining unique single strandedDNA strand and the 5′ end of the remaining unique reverse complementstrand; where i is a natural number having an initial value of 2 and nis a natural number having a value greater than 2.